module type S =`sig`

..`end`

Output signature of the functor `Extmap.Make`

.

`type `

key

The type of the map keys.

`type ``+'a`

t

The type of maps from type `key`

to type `'a`

.

`val empty : ``'a t`

The empty map.

`val is_empty : ``'a t -> bool`

Test whether a map is empty or not.

`val mem : ``key -> 'a t -> bool`

`mem x m`

returns `true`

if `m`

contains a binding for `x`

,
and `false`

otherwise.

`val add : ``key -> 'a -> 'a t -> 'a t`

`add x y m`

returns a map containing the same bindings as
`m`

, plus a binding of `x`

to `y`

. If `x`

was already bound
in `m`

, its previous binding disappears.

`val singleton : ``key -> 'a -> 'a t`

`singleton x y`

returns the one-element map that contains a binding `y`

for `x`

.

`val remove : ``key -> 'a t -> 'a t`

`remove x m`

returns a map containing the same bindings as
`m`

, except for `x`

which is unbound in the returned map.

`val merge : ``(key -> 'a option -> 'b option -> 'c option) ->`

'a t -> 'b t -> 'c t

`merge f m1 m2`

computes a map whose keys is a subset of keys of `m1`

and of `m2`

. The presence of each such binding, and the corresponding
value, is determined with the function `f`

.

`val union : ``(key -> 'a -> 'a -> 'a option) ->`

'a t -> 'a t -> 'a t

`union f m1 m2`

computes a map whose keys is a subset of keys
of `m1`

and of `m2`

. If a binding is present in `m1`

(resp. `m2`

)
and not in `m2`

(resp. `m1`

) the same binding is present in
the result. The function `f`

is called only in ambiguous cases.

`val compare : ``('a -> 'a -> int) -> 'a t -> 'a t -> int`

Total ordering between maps. The first argument is a total ordering used to compare data associated with equal keys in the two maps.

`val equal : ``('a -> 'a -> bool) -> 'a t -> 'a t -> bool`

`equal cmp m1 m2`

tests whether the maps `m1`

and `m2`

are
equal, that is, contain equal keys and associate them with
equal data. `cmp`

is the equality predicate used to compare
the data associated with the keys.

`val iter : ``(key -> 'a -> unit) -> 'a t -> unit`

`iter f m`

applies `f`

to all bindings in map `m`

.
`f`

receives the key as first argument, and the associated value
as second argument. The bindings are passed to `f`

in increasing
order with respect to the ordering over the type of the keys.

`val fold : ``(key -> 'a -> 'b -> 'b) -> 'a t -> 'b -> 'b`

`fold f m a`

computes `(f kN dN ... (f k1 d1 a)...)`

, where
`k1 ... kN`

are the keys of all bindings in `m`

(in increasing
order), and `d1 ... dN`

are the associated data.

`val for_all : ``(key -> 'a -> bool) -> 'a t -> bool`

`for_all p m`

checks if all the bindings of the map
satisfy the predicate `p`

.

`val exists : ``(key -> 'a -> bool) -> 'a t -> bool`

`exists p m`

checks if at least one binding of the map
satisfy the predicate `p`

.

`val filter : ``(key -> 'a -> bool) -> 'a t -> 'a t`

`filter p m`

returns the map with all the bindings in `m`

that satisfy predicate `p`

.

`val partition : ``(key -> 'a -> bool) ->`

'a t -> 'a t * 'a t

`partition p m`

returns a pair of maps `(m1, m2)`

, where
`m1`

contains all the bindings of `s`

that satisfy the
predicate `p`

, and `m2`

is the map with all the bindings of
`s`

that do not satisfy `p`

.

`val cardinal : ``'a t -> int`

Return the number of bindings of a map.

`val bindings : ``'a t -> (key * 'a) list`

Return the list of all bindings of the given map.
The returned list is sorted in increasing order with respect
to the ordering `Ord.compare`

, where `Ord`

is the argument
given to `Extmap.Make`

.

`val min_binding : ``'a t -> key * 'a`

Return the smallest binding of the given map
(with respect to the `Ord.compare`

ordering), or raise
`Not_found`

if the map is empty.

`val max_binding : ``'a t -> key * 'a`

Same as `Extmap.S.min_binding`

, but returns the largest
binding of the given map.

`val choose : ``'a t -> key * 'a`

Return one binding of the given map, or raise `Not_found`

if
the map is empty. Which binding is chosen is unspecified,
but equal bindings will be chosen for equal maps.

`val split : ``key -> 'a t -> 'a t * 'a option * 'a t`

`split x m`

returns a triple `(l, data, r)`

, where
`l`

is the map with all the bindings of `m`

whose key
is strictly less than `x`

;
`r`

is the map with all the bindings of `m`

whose key
is strictly greater than `x`

;
`data`

is `None`

if `m`

contains no binding for `x`

,
or `Some v`

if `m`

binds `v`

to `x`

.

`val find : ``key -> 'a t -> 'a`

`find x m`

returns the current binding of `x`

in `m`

,
or raises `Not_found`

if no such binding exists.

`val map : ``('a -> 'b) -> 'a t -> 'b t`

`map f m`

returns a map with same domain as `m`

, where
the associated value `a`

of all bindings of `m`

has been
replaced by the result of the application of `f`

to `a`

.
The bindings are passed to `f`

in increasing order
with respect to the ordering over the type of the keys.

`val mapi : ``(key -> 'a -> 'b) -> 'a t -> 'b t`

Same as `Extmap.S.map`

, but the function receives as arguments both
the key and the associated value for each binding of the map.

@Added in Why3

`val change : ``('a option -> 'a option) -> key -> 'a t -> 'a t`

`change f x m`

returns a map containing the same bindings as
`m`

, except the binding of `x`

in `m`

is changed from `y`

to
`f (Some y)`

if `m`

contains a binding of `x`

, otherwise the
binding of `x`

becomes `f None`

.

`change f x m`

corresponds to a more efficient way to do
```
match (try f (Some (find x m)) with Not_found -> f None) with
| None -> m
| Some v -> add x v
```

`val inter : ``(key -> 'a -> 'b -> 'c option) ->`

'a t -> 'b t -> 'c t

`inter f m1 m2`

computes a map whose keys is a subset of
the intersection of keys of `m1`

and of `m2`

.

`val diff : ``(key -> 'a -> 'b -> 'a option) ->`

'a t -> 'b t -> 'a t

`diff f m1 m2`

computes a map whose keys is a subset of keys
of `m1`

. `f`

is applied on key which belongs to `m1`

and `m2`

if `f`

returns `None`

the binding is removed from `m1`

,
otherwise `Some d1`

is returned, the key binds to `d1`

in `m1`

`val submap : ``(key -> 'a -> 'b -> bool) -> 'a t -> 'b t -> bool`

`submap pr m1 m2`

verifies that all the keys in m1 are in m2
and that for each such binding pr is verified.

`val disjoint : ``(key -> 'a -> 'b -> bool) -> 'a t -> 'b t -> bool`

`disjoint pr m1 m2`

verifies that for every common key in m1
and m2, pr is verified.

`val set_union : ``'a t -> 'a t -> 'a t`

`set_union = union (fun _ x _ -> Some x)`

`val set_inter : ``'a t -> 'b t -> 'a t`

`set_inter = inter (fun _ x _ -> Some x)`

`val set_diff : ``'a t -> 'b t -> 'a t`

`set_diff = diff (fun _ _ _ -> None)`

`val set_submap : ``'a t -> 'b t -> bool`

`set_submap = submap (fun _ _ _ -> true)`

`val set_disjoint : ``'a t -> 'b t -> bool`

`set_disjoint = disjoint (fun _ _ _ -> false)`

`val set_compare : ``'a t -> 'b t -> int`

`set_compare = compare (fun _ _ -> 0)`

`val set_equal : ``'a t -> 'b t -> bool`

`set_equal = equal (fun _ _ -> true)`

`val find_def : ``'a -> key -> 'a t -> 'a`

`find_def x d m`

returns the current binding of `x`

in `m`

,
or return `d`

if no such binding exists.

`val find_opt : ``key -> 'a t -> 'a option`

`find_opt x m`

returns the `Some`

of the current binding
of `x`

in `m`

, or return `None`

if no such binding exists.

`val find_exn : ``exn -> key -> 'a t -> 'a`

`find_exn exn x d m`

returns the current binding
of `x`

in `m`

, or raise `exn`

if no such binding exists.

`val map_filter : ``('a -> 'b option) -> 'a t -> 'b t`

Same as `Extmap.S.map`

, but may remove bindings.

`val mapi_filter : ``(key -> 'a -> 'b option) -> 'a t -> 'b t`

Same as `Extmap.S.mapi`

, but may remove bindings.

`val mapi_fold : ``(key -> 'a -> 'acc -> 'acc * 'b) ->`

'a t -> 'acc -> 'acc * 'b t

fold and map at the same time

`val mapi_filter_fold : ``(key -> 'a -> 'acc -> 'acc * 'b option) ->`

'a t -> 'acc -> 'acc * 'b t

Same as `Extmap.S.mapi_fold`

, but may remove bindings.

`val fold_left : ``('b -> key -> 'a -> 'b) -> 'b -> 'a t -> 'b`

same as `Extmap.S.fold`

but in the order of `List.fold_left`

`val fold2_inter : ``(key -> 'a -> 'b -> 'c -> 'c) ->`

'a t -> 'b t -> 'c -> 'c

fold the common keys of two map at the same time

`val fold2_union : ``(key -> 'a option -> 'b option -> 'c -> 'c) ->`

'a t -> 'b t -> 'c -> 'c

fold the keys which appear in one of the two maps

`val translate : ``(key -> key) -> 'a t -> 'a t`

`translate f m`

translates the keys in the map `m`

by the
function `f`

. `f`

must be strictly monotone on the key of `m`

.
Otherwise it raises invalid_arg

`val add_new : ``exn -> key -> 'a -> 'a t -> 'a t`

`add_new e x v m`

binds `x`

to `v`

in `m`

if `x`

is not bound,
and raises `e`

otherwise.

`val replace : ``exn -> key -> 'a -> 'a t -> 'a t`

`replace e x v m`

binds `x`

to `v`

in `m`

if `x`

is already bound,
and raises `e`

otherwise.

`val keys : ``'a t -> key list`

Return the list of all keys of the given map.
The returned list is sorted in increasing order with respect
to the ordering `Ord.compare`

, where `Ord`

is the argument
given to `Extmap.Make`

.

`val values : ``'a t -> 'a list`

Return the list of all values of the given map.
The returned list is sorted in increasing order with respect
to the ordering `Ord.compare`

of the keys, where `Ord`

is the argument
given to `Extmap.Make`

.

`val of_list : ``(key * 'a) list -> 'a t`

construct a map from a list of bindings.

`val contains : ``'a t -> key -> bool`

`contains m x`

is the same as `mem x m`

.

`val domain : ``'a t -> unit t`

`domain m`

returns the set of keys of bindings in `m`

`val subdomain : ``(key -> 'a -> bool) -> 'a t -> unit t`

`subdomain pr m`

returns the set of keys of bindings in `m`

that satisfy predicate `pr`

`val is_num_elt : ``int -> 'a t -> bool`

check if the map has the given number of elements

`type ``'a`

enumeration

enumeration: zipper style

`val val_enum : ``'a enumeration -> (key * 'a) option`

get the current key value pair of the enumeration, return None if the enumeration reach the end

`val start_enum : ``'a t -> 'a enumeration`

start the enumeration of the given map

`val next_enum : ``'a enumeration -> 'a enumeration`

get the next step of the enumeration

`val start_ge_enum : ``key -> 'a t -> 'a enumeration`

start the enumeration of the given map at the first key which is greater or equal than the given one

`val next_ge_enum : ``key -> 'a enumeration -> 'a enumeration`

get the next (or same) step of the enumeration which key is greater or equal to the given key